Answer :
Sure! Let's solve the equation step by step:
The equation given is:
[tex]\[ 4|x+5| + 8 = 24 \][/tex]
### Step 1: Isolate the Absolute Value
First, subtract 8 from both sides of the equation to get:
[tex]\[ 4|x+5| = 24 - 8 \][/tex]
[tex]\[ 4|x+5| = 16 \][/tex]
### Step 2: Solve for the Absolute Value
Divide both sides by 4 to isolate [tex]\(|x+5|\)[/tex]:
[tex]\[ |x+5| = \frac{16}{4} \][/tex]
[tex]\[ |x+5| = 4 \][/tex]
### Step 3: Solve the Absolute Value Equation
The equation [tex]\(|x+5| = 4\)[/tex] means there are two possible cases:
Case 1:
[tex]\[ x + 5 = 4 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 4 - 5 \][/tex]
[tex]\[ x = -1 \][/tex]
Case 2:
[tex]\[ x + 5 = -4 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -4 - 5 \][/tex]
[tex]\[ x = -9 \][/tex]
### Conclusion
The solutions to the equation [tex]\(4|x+5| + 8 = 24\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
So the correct answer is:
D. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]
The equation given is:
[tex]\[ 4|x+5| + 8 = 24 \][/tex]
### Step 1: Isolate the Absolute Value
First, subtract 8 from both sides of the equation to get:
[tex]\[ 4|x+5| = 24 - 8 \][/tex]
[tex]\[ 4|x+5| = 16 \][/tex]
### Step 2: Solve for the Absolute Value
Divide both sides by 4 to isolate [tex]\(|x+5|\)[/tex]:
[tex]\[ |x+5| = \frac{16}{4} \][/tex]
[tex]\[ |x+5| = 4 \][/tex]
### Step 3: Solve the Absolute Value Equation
The equation [tex]\(|x+5| = 4\)[/tex] means there are two possible cases:
Case 1:
[tex]\[ x + 5 = 4 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 4 - 5 \][/tex]
[tex]\[ x = -1 \][/tex]
Case 2:
[tex]\[ x + 5 = -4 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -4 - 5 \][/tex]
[tex]\[ x = -9 \][/tex]
### Conclusion
The solutions to the equation [tex]\(4|x+5| + 8 = 24\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
So the correct answer is:
D. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]